I suggest that, on a database by database basis, you create a role to do this. Give the role DDL privileges and backup privileges.
exec sp_addrole 'DDL_And_Backup_Role'
exec sp_addrolemember 'db_ddladmin' ,'DDL_And_Backup_Role'
GRANT BACKUP DATABASE TO DDL_And_Backup_Role
Add your user to this role in the selected databases.
Cheers,
- Mark